(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    137518,       4443]
NotebookOptionsPosition[    130020,       4320]
NotebookOutlinePosition[    130591,       4341]
CellTagsIndexPosition[    130548,       4338]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Initialization", "Section",
 CellChangeTimes->{{3.622898427212637*^9, 
  3.6228984354978595`*^9}},ExpressionUUID->"132e4493-406b-4308-8399-\
c3bf8ea88b51"],

Cell[BoxData[
 RowBox[{
  RowBox[{"SetDirectory", "[", 
   RowBox[{"NotebookDirectory", "[", "]"}], "]"}], ";"}]], "Input",
 CellChangeTimes->{{3.6228983913429365`*^9, 3.6228984011503663`*^9}, 
   3.761257919995492*^9},
 CellLabel->"In[1]:=",ExpressionUUID->"9e4172bc-bde2-4648-ae13-44c16a1f17a1"],

Cell[BoxData[
 RowBox[{"<<", "InputS3SixJSymbols.mx"}]], "Input",
 CellChangeTimes->{{3.6228985346205287`*^9, 3.622898556351186*^9}, {
  3.6274265646808777`*^9, 3.6274265754312973`*^9}, {3.6274266122407618`*^9, 
  3.627426626281787*^9}, {3.7612536804467764`*^9, 3.7612536806901693`*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"81ab6ff9-ca9a-4954-9600-2e9e961cc842"],

Cell[CellGroupData[{

Cell["Formats", "Subsection",
 CellChangeTimes->{{3.769247572915351*^9, 
  3.769247574447255*^9}},ExpressionUUID->"724d96c4-149e-49ae-8f53-\
191d21a8ab3a"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Format", "[", 
   RowBox[{
    RowBox[{"f", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"a_", ",", "b_"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"c_", ",", "d_"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"e_", ",", "f1_"}], "}"}]}], "]"}], ",", "TraditionalForm"}], 
   "]"}], ":=", 
  RowBox[{"f", "[", 
   RowBox[{
    SubscriptBox["a", "b"], ",", 
    SubscriptBox["c", "d"], ",", 
    SubscriptBox["e", "f1"]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.7612523015450644`*^9, 3.761252402587423*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"7e9b4097-c922-49b8-bcab-752c6b187e59"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"pair", "/:", 
   RowBox[{"MakeBoxes", "[", 
    RowBox[{
     RowBox[{"pair", "[", 
      RowBox[{"a_", ",", "b_"}], "]"}], ",", "TraditionalForm"}], "]"}], ":=", 
   RowBox[{"RowBox", "[", 
    RowBox[{"{", 
     RowBox[{"\"\<[\>\"", ",", 
      RowBox[{"stringForm", "[", 
       RowBox[{"a", ",", "b"}], "]"}], ",", "\"\<]\>\""}], "}"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "/:", 
   RowBox[{"MakeBoxes", "[", 
    RowBox[{
     RowBox[{"G", "[", 
      RowBox[{"a_", ",", "b_", ",", "c_", ",", "d_", ",", "e_", ",", "f_"}], 
      "]"}], ",", "TraditionalForm"}], "]"}], ":=", 
   RowBox[{"SubsuperscriptBox", "[", 
    RowBox[{"\"\<G\>\"", ",", 
     RowBox[{"stringForm", "[", 
      RowBox[{"d", ",", "e", ",", "f"}], "]"}], ",", 
     RowBox[{"stringForm", "[", 
      RowBox[{"a", ",", "b", ",", "c"}], "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"f", "/:", 
   RowBox[{"MakeBoxes", "[", 
    RowBox[{
     RowBox[{"f", "[", 
      RowBox[{"a_", ",", "b_", ",", "c_"}], "]"}], ",", "TraditionalForm"}], 
    "]"}], ":=", 
   RowBox[{"SubscriptBox", "[", 
    RowBox[{"\"\<f\>\"", ",", 
     RowBox[{"stringForm", "[", 
      RowBox[{"a", ",", "b", ",", "c"}], "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"vv", "/:", 
   RowBox[{"MakeBoxes", "[", 
    RowBox[{
     RowBox[{"vv", "[", "a_", "]"}], ",", "TraditionalForm"}], "]"}], ":=", 
   RowBox[{"SubscriptBox", "[", 
    RowBox[{"\"\<v\>\"", ",", 
     RowBox[{"MakeBoxes", "[", 
      RowBox[{"a", ",", "TraditionalForm"}], "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dd", "/:", 
   RowBox[{"MakeBoxes", "[", 
    RowBox[{
     RowBox[{"dd", "[", "a_", "]"}], ",", "TraditionalForm"}], "]"}], ":=", 
   RowBox[{"SubscriptBox", "[", 
    RowBox[{"\"\<d\>\"", ",", 
     RowBox[{"MakeBoxes", "[", 
      RowBox[{"a", ",", "TraditionalForm"}], "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"stringForm", "[", 
    RowBox[{"a__", "?", "NumericQ"}], "]"}], ":=", 
   RowBox[{"StringJoin", "@@", 
    RowBox[{"(", 
     RowBox[{"ToString", "/@", 
      RowBox[{"{", "a", "}"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"stringForm", "[", "a__", "]"}], ":=", 
   RowBox[{"StringJoin", "[", 
    RowBox[{"ToString", "/@", 
     RowBox[{"TraditionalForm", "/@", 
      RowBox[{"{", "a", "}"}]}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.7689955577343774`*^9, 3.7689956432523584`*^9}, {
  3.768995907271965*^9, 3.768995981462122*^9}, {3.768996042798726*^9, 
  3.7689960953616467`*^9}, {3.768996204216971*^9, 3.768996212870301*^9}, {
  3.768997593289139*^9, 3.7689976248662853`*^9}, {3.768997663273836*^9, 
  3.7689977638990326`*^9}, {3.7689977998011174`*^9, 3.76899782201527*^9}, {
  3.7689991022420826`*^9, 3.768999103677245*^9}, {3.769000549793692*^9, 
  3.7690005610460677`*^9}, {3.7690006006508236`*^9, 3.769000661927194*^9}, {
  3.7690032522897377`*^9, 3.7690032561609883`*^9}, {3.769247625815283*^9, 
  3.7692476261753283`*^9}, {3.7692476578311076`*^9, 3.7692476603360977`*^9}, {
  3.7692591221398706`*^9, 3.7692591295447373`*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"ea16ee10-22ab-4a3c-8ff8-50ff9985785c"],

Cell["Example code:", "Text",
 CellChangeTimes->{{3.76925941915464*^9, 
  3.7692594215372686`*^9}},ExpressionUUID->"f5370a3d-88d1-4d53-880f-\
e4ac59f6d10b"],

Cell["\<\
Input := {pair[1, 2], G[1, 2, 3, 4, 5, 6], f[1, 2, 3], vv[1], dd[1]}\
\>", "Program",
 CellChangeTimes->{{3.7692568890423613`*^9, 3.7692569370800257`*^9}, {
   3.7692570390121613`*^9, 3.7692570690767612`*^9}, {3.7692572755504456`*^9, 
   3.76925730221739*^9}, 3.7692575181804934`*^9},
 Background->None,ExpressionUUID->"15474eb2-a3df-4e8c-8c5d-885fd0ed7de6"],

Cell[BoxData[
 FormBox[
  RowBox[{"Output", ":=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"[", "12", "]"}], ",", 
     SubsuperscriptBox["G", "123", "456"], ",", 
     SubscriptBox["f", "123"], ",", 
     SubscriptBox["v", "1"], ",", 
     SubscriptBox["d", "1"]}], "}"}]}], TraditionalForm]], "Program",
 CellChangeTimes->{{3.769256892513563*^9, 3.769256937122948*^9}, 
   3.7692570253252993`*^9, {3.769257072046451*^9, 3.7692570747556477`*^9}, {
   3.7692572223712893`*^9, 3.769257252238117*^9}, {3.769257293528197*^9, 
   3.7692573005133224`*^9}, 3.7692575202734537`*^9},
 Background->None,ExpressionUUID->"0166f5e8-a0cd-4911-b13b-1cfb98ffee6c"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Grammer Sugar Tools", "Subsection",
 CellChangeTimes->{{3.7692508658605824`*^9, 
  3.7692508808129797`*^9}},ExpressionUUID->"fc3a3eb1-0373-43f1-b9b7-\
ae025de72511"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"uFlatten", "=", 
   RowBox[{"Union", "@*", "Flatten"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"over", "[", 
    RowBox[{"tabName_", ",", "rng_"}], "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"tab", ",", "xlist", ",", "a", ",", "x"}], "}"}], ",", 
     RowBox[{
      RowBox[{"SetAttributes", "[", 
       RowBox[{"tab", ",", "HoldAll"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tab", "[", 
        RowBox[{"a_", ",", "x__"}], "]"}], ":=", 
       RowBox[{"Block", "[", 
        RowBox[{
         RowBox[{"{", "x", "}"}], ",", 
         RowBox[{
          RowBox[{"xlist", "=", 
           RowBox[{"Sequence", "@@", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{"{", 
                RowBox[{"#", ",", "rng"}], "}"}], "&"}], "/@", 
              RowBox[{"{", "x", "}"}]}], ")"}]}]}], ";", 
          RowBox[{"tabName", "[", 
           RowBox[{"a", ",", 
            RowBox[{"Evaluate", "@", "xlist"}]}], "]"}]}]}], "]"}]}], ";", 
      "\[IndentingNewLine]", "tab"}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.769250941195943*^9, 3.7692509516065884`*^9}, {
   3.7692512711709366`*^9, 3.769251283034628*^9}, {3.7692514226358967`*^9, 
   3.769251477180873*^9}, {3.7692515100559444`*^9, 3.7692515663460627`*^9}, {
   3.7692516089007745`*^9, 3.769251720859778*^9}, {3.7692518662948866`*^9, 
   3.769251875035186*^9}, {3.7692523903945956`*^9, 3.769252439433565*^9}, {
   3.7692524877607536`*^9, 3.7692524990571337`*^9}, {3.7692526372223177`*^9, 
   3.7692526455553856`*^9}, {3.7692527747111683`*^9, 3.7692528083327217`*^9}, 
   3.7692568390286045`*^9},
 CellLabel->"In[11]:=",ExpressionUUID->"e1a2d00d-55aa-48ff-be81-8eb442de04c4"],

Cell["Example code:", "Text",
 CellChangeTimes->{{3.769259398895151*^9, 
  3.7692594018371167`*^9}},ExpressionUUID->"1c85a93a-e29a-4cfc-b0df-\
52bd1af9a438"],

Cell["Input := (Table~over~{11, 22, 33})[test[x, y], x, y]", "Program",
 CellChangeTimes->{{3.769257385620988*^9, 
  3.7692575234339933`*^9}},ExpressionUUID->"99826ed3-794d-4221-bfa2-\
c90bc43b5757"],

Cell[BoxData[
 FormBox[
  RowBox[{"Output", ":=", " ", 
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"test", "(", 
        RowBox[{"11", ",", "11"}], ")"}], 
       RowBox[{"test", "(", 
        RowBox[{"11", ",", "22"}], ")"}], 
       RowBox[{"test", "(", 
        RowBox[{"11", ",", "33"}], ")"}]},
      {
       RowBox[{"test", "(", 
        RowBox[{"22", ",", "11"}], ")"}], 
       RowBox[{"test", "(", 
        RowBox[{"22", ",", "22"}], ")"}], 
       RowBox[{"test", "(", 
        RowBox[{"22", ",", "33"}], ")"}]},
      {
       RowBox[{"test", "(", 
        RowBox[{"33", ",", "11"}], ")"}], 
       RowBox[{"test", "(", 
        RowBox[{"33", ",", "22"}], ")"}], 
       RowBox[{"test", "(", 
        RowBox[{"33", ",", "33"}], ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}]}], TraditionalForm]], "Program",
 CellChangeTimes->{{3.7692574379617195`*^9, 
  3.76925751366397*^9}},ExpressionUUID->"47439685-50e6-4681-8788-\
8098dc6d3937"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Define data", "Subsection",
 CellChangeTimes->{{3.6228993656241612`*^9, 
  3.622899372203377*^9}},ExpressionUUID->"d062233e-ab35-436c-8397-\
4f624d662e24"],

Cell[TextData[{
 StyleBox["basis data of ",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 Cell[BoxData[
  FormBox[
   SubscriptBox["Rep", 
    SubscriptBox["S", "3"]], TraditionalForm]],
  FormatType->"TraditionalForm",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88],ExpressionUUID->
  "2145f8e1-8388-4d2e-908a-b8d528685f13"]
}], "Text",
 CellChangeTimes->{{3.769259771891965*^9, 
  3.769259780624382*^9}},ExpressionUUID->"6476039f-c022-4201-9ed5-\
c73fa8551f6d"],

Cell[BoxData[
 RowBox[{
  RowBox[{"rng", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.622899527397588*^9, 3.622899530915797*^9}, {
  3.62742700787507*^9, 3.6274270099966736`*^9}, {3.7612536977504997`*^9, 
  3.761253699874862*^9}},
 CellLabel->"In[13]:=",ExpressionUUID->"1275223a-9d3c-4510-81af-6c33d2a1ba15"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"v", "[", "1", "]"}], "=", "1"}], ";", 
  RowBox[{
   RowBox[{"v", "[", "2", "]"}], "=", "1"}], ";", 
  RowBox[{
   RowBox[{"v", "[", "3", "]"}], "=", 
   SqrtBox["2"]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"v", "[", 
    RowBox[{"{", 
     RowBox[{"a_Integer", ",", "b_"}], "}"}], "]"}], ":=", 
   RowBox[{"v", "[", "a", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"dim", "[", "j_", "]"}], ":=", 
   RowBox[{
    RowBox[{"v", "[", "j", "]"}], "^", "2"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"delt", "[", 
    RowBox[{"i_Integer", ",", "j_Integer", ",", "k_Integer"}], "]"}], ":=", 
   RowBox[{
    RowBox[{"delt", "[", 
     RowBox[{"i", ",", "j", ",", "k"}], "]"}], "=", 
    RowBox[{
     RowBox[{
      RowBox[{"v", "[", "j", "]"}], 
      RowBox[{"v", "[", "k", "]"}], 
      RowBox[{"mTet", "[", 
       RowBox[{"i", ",", "j", ",", "k", ",", "1", ",", "k", ",", "j"}], 
       "]"}]}], "//", "FullSimplify"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"delt", "[", 
    RowBox[{"a___", ",", 
     RowBox[{"{", 
      RowBox[{"b_Integer", ",", "c_"}], "}"}], ",", "d___"}], "]"}], ":=", 
   RowBox[{"delt", "[", 
    RowBox[{"a", ",", "b", ",", "d"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"mTet", "[", 
    RowBox[{"a___", ",", 
     RowBox[{"{", 
      RowBox[{"b_", ",", "c_"}], "}"}], ",", "d___"}], "]"}], ":=", 
   RowBox[{"mTet", "[", 
    RowBox[{"a", ",", "b", ",", "d"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"mTet", "[", "a__Integer", "]"}], ":=", 
   RowBox[{"Tet", "[", "a", "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.6228993758433857`*^9, 3.622899452527793*^9}, {
   3.6228994879016895`*^9, 3.6228995227049756`*^9}, {3.627427015659484*^9, 
   3.6274270391465254`*^9}, {3.6274274799277225`*^9, 
   3.6274275297808104`*^9}, {3.761253736364359*^9, 3.7612537434054995`*^9}, 
   3.7690012335252886`*^9, 3.769001332328216*^9, {3.7690013691462708`*^9, 
   3.76900137122924*^9}, {3.7692013486693163`*^9, 3.7692013712875214`*^9}, {
   3.7692096407960615`*^9, 3.769209646942066*^9}, {3.769247468977762*^9, 
   3.769247482950234*^9}, {3.769247894672099*^9, 3.769247950047741*^9}, {
   3.7692507755955667`*^9, 3.769250790813882*^9}},
 CellLabel->"In[14]:=",ExpressionUUID->"693f93e7-df28-422e-ab77-b288ba00ed27"],

Cell[TextData[StyleBox["mTet[...] is the 6j-symbol",
 FontColor->RGBColor[1, 0, 1],
 Background->RGBColor[0.94, 0.91, 0.88]]], "Text",
 CellChangeTimes->{{3.769257640924214*^9, 
  3.7692576564096966`*^9}},ExpressionUUID->"15f29ffb-a0de-4803-a6b6-\
7980e92cb94e"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"triples", "[", "Arng_", "]"}], ":=", 
   RowBox[{"f", "@@@", 
    RowBox[{"Tuples", "[", 
     RowBox[{"Arng", ",", "3"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"fusionTriples", "[", "Arng_", "]"}], ":=", 
   RowBox[{
    RowBox[{"Select", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"delt", "@@", "#"}], "\[Equal]", "1"}], "&"}], "]"}], "@", 
    RowBox[{"triples", "[", "Arng", "]"}]}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.769247837314223*^9, 3.7692478739131684`*^9}, {
  3.7692479238107643`*^9, 3.7692479258986964`*^9}, {3.769248040365491*^9, 
  3.769248045095421*^9}, {3.7692505790665493`*^9, 3.769250613560217*^9}, {
  3.7692506978099384`*^9, 3.769250716902742*^9}},
 CellLabel->"In[21]:=",ExpressionUUID->"775cbdb4-e11a-407a-a954-f3da23689fb5"],

Cell[BoxData[
 RowBox[{
  RowBox[{"subrng", "[", "n_", "]"}], ":=", 
  RowBox[{"Select", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"#", "[", 
      RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", "n"}], "&"}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.760920766858997*^9, 3.7609208033619633`*^9}, {
  3.76920139602489*^9, 3.7692014000676394`*^9}, {3.7692092675909033`*^9, 
  3.769209274324673*^9}},
 CellLabel->"In[23]:=",ExpressionUUID->"a87ae13f-f866-4de8-b286-e6a69eb5d105"],

Cell[BoxData[
 RowBox[{
  RowBox[{"unit", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "1"}], "}"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.7692482287524595`*^9, 3.769248277864888*^9}, {
   3.769248380138666*^9, 3.769248393184214*^9}, {3.769248953272343*^9, 
   3.769248962082036*^9}, 3.769250846414651*^9, {3.769253338810543*^9, 
   3.7692533396722307`*^9}},
 CellLabel->"In[24]:=",ExpressionUUID->"da788df7-0e8b-4f92-a8f2-7951243cf2d5"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"fusionCondition", "[", "Arng_", "]"}], ":=", 
   RowBox[{
    RowBox[{
     RowBox[{"Complement", "[", 
      RowBox[{
       RowBox[{"triples", "[", "Arng", "]"}], ",", 
       RowBox[{"fusionTriples", "[", "Arng", "]"}]}], "]"}], "\[Rule]", "0"}],
     "//", "Thread"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"nonDegeneracyCondition", "[", "Arng_", "]"}], ":=", 
   RowBox[{"uFlatten", "@", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"f", "[", 
        RowBox[{"unit", ",", "i", ",", "j"}], "]"}], "\[Rule]", 
       RowBox[{"KroneckerDelta", "[", 
        RowBox[{"i", ",", "j"}], "]"}]}], ",", 
      RowBox[{"{", 
       RowBox[{"i", ",", "Arng"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"j", ",", "Arng"}], "}"}]}], "]"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"fusionReplace", "[", "Arng_", "]"}], ":=", 
   RowBox[{
    RowBox[{"fusionReplace", "[", "Arng", "]"}], "=", 
    RowBox[{"ReplaceAll", "[", 
     RowBox[{
      RowBox[{"fusionCondition", "[", "Arng", "]"}], "\[Union]", 
      RowBox[{"nonDegeneracyCondition", "[", "Arng", "]"}]}], "]"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"cyclicCondition", "[", "Arng_", "]"}], ":=", 
   RowBox[{
    RowBox[{"Thread", "/@", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"Rest", "@", "#"}], "\[Rule]", 
         RowBox[{
          RowBox[{"fusionReplace", "[", "Arng", "]"}], "@", 
          RowBox[{"First", "@", "#"}]}]}], "&"}], ")"}], "/@", 
      RowBox[{
       RowBox[{"Select", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"Length", "[", "#", "]"}], ">", "1"}], "&"}], "]"}], "@", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"Union", "[", 
           RowBox[{"NestList", "[", 
            RowBox[{"RotateLeft", ",", "#", ",", "2"}], "]"}], "]"}], "&"}], "/@", 
         RowBox[{"f", "@@@", 
          RowBox[{"Tuples", "[", 
           RowBox[{"Arng", ",", "3"}], "]"}]}]}], ")"}]}]}]}], "//", 
    "uFlatten"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.7692479811811447`*^9, 3.769247992895161*^9}, {
   3.76924808154471*^9, 3.7692480829739027`*^9}, {3.7692481438838396`*^9, 
   3.7692481469850597`*^9}, {3.769248178846511*^9, 3.7692481827450843`*^9}, {
   3.7692483045584764`*^9, 3.769248435072155*^9}, {3.769248574200316*^9, 
   3.769248574937725*^9}, {3.7692487091001377`*^9, 3.7692487158112006`*^9}, {
   3.7692489722004004`*^9, 3.769248973226703*^9}, {3.7692493518065944`*^9, 
   3.769249371638497*^9}, {3.7692495205186605`*^9, 3.76924956518028*^9}, {
   3.7692496514867835`*^9, 3.7692496650062456`*^9}, {3.769249712620964*^9, 
   3.7692497210095053`*^9}, {3.769249782879037*^9, 3.769249813058446*^9}, {
   3.7692498506770315`*^9, 3.7692498593781376`*^9}, 3.7692498929574547`*^9, {
   3.769249925539568*^9, 3.769249997272215*^9}, {3.7692501400399694`*^9, 
   3.769250148566368*^9}, {3.7692502119066567`*^9, 3.769250215417555*^9}, {
   3.7692502487125263`*^9, 3.7692502560196342`*^9}, {3.7692503976489124`*^9, 
   3.7692504032420187`*^9}, {3.7692505269344935`*^9, 3.769250566674469*^9}, {
   3.7692506200321684`*^9, 3.7692506293488*^9}, {3.769250814920249*^9, 
   3.769250822167477*^9}, {3.7692526526818724`*^9, 3.769252655708042*^9}, {
   3.7692533426418653`*^9, 3.7692533436870704`*^9}, 3.7692548434881215`*^9, {
   3.7692548847792964`*^9, 3.7692549514652214`*^9}, {3.769255003011003*^9, 
   3.7692550230035973`*^9}},
 CellLabel->"In[25]:=",ExpressionUUID->"d17c2cc3-2389-478f-a9aa-dccb6c2eaa37"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"symmetryCondition", "[", "Arng_", "]"}], ":=", 
   RowBox[{
    RowBox[{"symmetryCondition", "[", "Arng", "]"}], "=", 
    RowBox[{
     RowBox[{"fusionCondition", "[", "Arng", "]"}], "\[Union]", 
     RowBox[{"nonDegeneracyCondition", "[", "Arng", "]"}], "\[Union]", 
     RowBox[{"cyclicCondition", "[", "Arng", "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"symmetryReplace", "[", "Arng_", "]"}], ":=", 
   RowBox[{"ReplaceRepeated", "[", 
    RowBox[{"symmetryCondition", "[", "Arng", "]"}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.7692527048426285`*^9, 3.769252745781379*^9}, {
  3.769255089311986*^9, 3.769255120194982*^9}},
 CellLabel->"In[29]:=",ExpressionUUID->"f5532cde-9b8d-4cc9-b0de-274b901d924f"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"fEquations", "[", "Arng_", "]"}], ":=", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"(", 
        RowBox[{"Table", "~", "over", "~", "Arng"}], ")"}], "[", 
       RowBox[{
        RowBox[{"Table", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"Sum", "[", 
            RowBox[{
             RowBox[{
              RowBox[{"f", "[", 
               RowBox[{"a", ",", "gl", ",", "e"}], "]"}], 
              RowBox[{"f", "[", 
               RowBox[{"b", ",", "d", ",", "gl"}], "]"}]}], ",", 
             RowBox[{"{", 
              RowBox[{"gl", ",", 
               RowBox[{
                RowBox[{"subrng", "[", "g", "]"}], "[", "Arng", "]"}]}], 
              "}"}]}], "]"}], "\[Equal]", 
           RowBox[{"Sum", "[", 
            RowBox[{
             RowBox[{
              RowBox[{"mTet", "[", 
               RowBox[{
               "a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "g"}], "]"}], 
              RowBox[{"v", "[", "c", "]"}], 
              RowBox[{"v", "[", "g", "]"}], 
              RowBox[{"f", "[", 
               RowBox[{"a", ",", "b", ",", "c"}], "]"}], 
              RowBox[{"f", "[", 
               RowBox[{"c", ",", "d", ",", "e"}], "]"}]}], ",", 
             RowBox[{"{", 
              RowBox[{"c", ",", "Arng"}], "}"}]}], "]"}]}], ",", 
          RowBox[{"{", 
           RowBox[{"g", ",", "rng"}], "}"}]}], "]"}], ",", "a", ",", "b", ",",
         "d", ",", "e"}], "]"}], "//", 
      RowBox[{"symmetryReplace", "[", "Arng", "]"}]}], "//", "uFlatten"}], "//",
     "Simplify"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.761259334399796*^9, 3.7612593548964005`*^9}, {
   3.7612593992902718`*^9, 3.7612594648356037`*^9}, {3.7612997460829673`*^9, 
   3.761299747742257*^9}, {3.7612999446544223`*^9, 3.7612999482810163`*^9}, 
   3.7691955218828683`*^9, {3.769195579122141*^9, 3.7691955846047087`*^9}, 
   3.769195744820468*^9, {3.769252823323656*^9, 3.7692528336670055`*^9}, {
   3.769252864627019*^9, 3.76925290015327*^9}, {3.7692532568046055`*^9, 
   3.7692532612793264`*^9}, 3.769253320075124*^9, {3.7692534060097227`*^9, 
   3.769253426979786*^9}},
 CellLabel->"In[31]:=",ExpressionUUID->"f72d4a6e-35cc-4236-a746-7cbae7b24f60"]
}, Open  ]],

Cell[CellGroupData[{

Cell["GSD formula", "Subsection",
 CellChangeTimes->{{3.769187851580071*^9, 3.7691878536618614`*^9}, {
  3.769196627067766*^9, 3.7691966279733496`*^9}, {3.769256368509634*^9, 
  3.76925637025373*^9}},ExpressionUUID->"35a69115-fb7e-4cfa-95db-\
d287edb75b84"],

Cell[TextData[{
 StyleBox["The periodic identification ",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"748734", "\[Rule]", "615621"}], ",", 
    RowBox[{"41581", "\[Rule]", "32672"}]}], TraditionalForm]],
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88],ExpressionUUID->
  "6001e960-eab2-4ee0-b985-de55555645fc"],
 StyleBox[", , a such that  labels [74],[48],,[87]... are identified as \
[61],[15],[56]... see the cubic-triangulation picture in my note.",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]]
}], "Text",
 CellChangeTimes->{{3.7692008542275715`*^9, 3.7692008774613323`*^9}, {
  3.769210878543024*^9, 3.7692109731815643`*^9}, {3.769259253385392*^9, 
  3.769259295591934*^9}},ExpressionUUID->"bd6f3f66-2730-4f53-a9ab-\
4d4b25b0350a"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"starReplace", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"aa_pair", "/;", 
      RowBox[{"!", 
       RowBox[{"OrderedQ", "[", "aa", "]"}]}]}], "\[RuleDelayed]", 
     RowBox[{"SuperStar", "[", 
      RowBox[{"Reverse", "[", "aa", "]"}], "]"}]}], "//", "ReplaceAll"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"periodicReplace", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"Module", "[", 
     RowBox[{
      RowBox[{"{", "interpretation", "}"}], ",", "\[IndentingNewLine]", "  ", 
      RowBox[{
       RowBox[{
        RowBox[{"interpretation", "[", "n_", "]"}], " ", ":=", " ", 
        RowBox[{
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"pair", "@", "##"}], ",", " ", 
            RowBox[{"Reverse", "@", 
             RowBox[{"pair", "@", "##"}]}]}], "}"}], " ", "&"}], " ", "@@@", 
         RowBox[{"Partition", "[", 
          RowBox[{
           RowBox[{"IntegerDigits", "[", "n", "]"}], ",", " ", "2", ",", " ", 
           "1"}], "]"}]}]}], ";", "\n", "  ", 
       RowBox[{
        RowBox[{"Thread", "@*", 
         RowBox[{"Map", "[", 
          RowBox[{"Flatten", "@*", "interpretation"}], "]"}]}], " ", "/@", 
        " ", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"748734", " ", "->", " ", "615621"}], ",", 
          RowBox[{"41581", "\[Rule]", "32672"}]}], "}"}]}]}]}], "]"}], " ", "//",
     " ", "uFlatten"}], "//", "ReplaceRepeated"}]}]}], "Input",
 CellChangeTimes->CompressedData["
1:eJxTTMoPSmViYGAQA2IQrVXBrXBS5I3j4zktiiCaIfqOKohua/usBaJjlYz0
QTT7i2AwvS57uTGI7lPRdQfRPf2rH4Bo1i96X0G0Sgj/TxBdsno5+ykgXSO+
3xFEr9yk4AWiJXR7GkH029nSHSD6TPO9HhB95YlHL5g/8fhUEH1gAvNMEL1g
Jv8iEH15QtESEN3AIKxzBUgzbUwB0x5/Ey1AdFblfDBtcO5kHYje45RSD6KX
smnUaYi+cVRT+tQCosXquLpA9I9J17tBtDX/seO6QLpJSegEiOZqeKahB6R/
NfFogugfXg4ixkC67cwdKRB96eIxJRDt99tKE0TLLS12BdGnwnrdQLTEk4V/
3IH006/O/0A0ADVepCk=
  "],
 CellLabel->"In[32]:=",ExpressionUUID->"cad7a18d-5ba0-4426-b6fe-afb1e104bad8"],

Cell[BoxData[
 FormBox[
  RowBox[{"ReplaceRepeated", "[", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"[", "14", "]"}], "\[Rule]", 
      RowBox[{"[", "23", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "15", "]"}], "\[Rule]", 
      RowBox[{"[", "26", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "18", "]"}], "\[Rule]", 
      RowBox[{"[", "27", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "34", "]"}], "\[Rule]", 
      RowBox[{"[", "21", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "37", "]"}], "\[Rule]", 
      RowBox[{"[", "26", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "41", "]"}], "\[Rule]", 
      RowBox[{"[", "32", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "43", "]"}], "\[Rule]", 
      RowBox[{"[", "12", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "47", "]"}], "\[Rule]", 
      RowBox[{"[", "16", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "48", "]"}], "\[Rule]", 
      RowBox[{"[", "15", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "51", "]"}], "\[Rule]", 
      RowBox[{"[", "62", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "58", "]"}], "\[Rule]", 
      RowBox[{"[", "67", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "73", "]"}], "\[Rule]", 
      RowBox[{"[", "62", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "74", "]"}], "\[Rule]", 
      RowBox[{"[", "61", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "78", "]"}], "\[Rule]", 
      RowBox[{"[", "65", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "81", "]"}], "\[Rule]", 
      RowBox[{"[", "72", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "84", "]"}], "\[Rule]", 
      RowBox[{"[", "51", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "85", "]"}], "\[Rule]", 
      RowBox[{"[", "76", "]"}]}], ",", 
     RowBox[{
      RowBox[{"[", "87", "]"}], "\[Rule]", 
      RowBox[{"[", "56", "]"}]}]}], "}"}], "]"}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.768995727181049*^9, 3.768995754045312*^9}, {
   3.7689958066832113`*^9, 3.768995854597106*^9}, 3.768995902210125*^9, 
   3.768995985413149*^9, {3.768996055249689*^9, 3.768996097379835*^9}, 
   3.7689962145143476`*^9, {3.768996383982158*^9, 3.7689964338944464`*^9}, 
   3.76899697085741*^9, 3.7689970663076115`*^9, {3.7689971406449146`*^9, 
   3.768997156817379*^9}, 3.768997847690522*^9, 3.7689988057869253`*^9, 
   3.768998961000452*^9, 3.768999125524187*^9, 3.7690154136124268`*^9, 
   3.7690166936340313`*^9, 3.7690167734752407`*^9, 3.7690173406432095`*^9, 
   3.769184191604389*^9, 3.7691875959988985`*^9, {3.7691879159321966`*^9, 
   3.7691879414027805`*^9}, 3.769189471588085*^9, 3.769189930857605*^9, 
   3.769189965799867*^9, 3.769190006576327*^9, 3.7691967650812597`*^9, 
   3.7691968213869133`*^9, 3.769196875535722*^9, 3.769196979400323*^9, 
   3.769197085761679*^9, {3.7691971563865676`*^9, 3.769197172567383*^9}, {
   3.7692009553457203`*^9, 3.7692009690788336`*^9}, 3.769201252000743*^9, 
   3.76921023896601*^9, 3.7692112115883217`*^9, 3.7692114448703012`*^9, 
   3.7692119510675163`*^9, 3.7692120303862505`*^9, 3.7692552273966007`*^9, 
   3.7692564024377184`*^9, 3.769256446587801*^9, 3.769256865696333*^9, 
   3.7692591336269755`*^9, 3.7692602125940886`*^9},
 CellLabel->"Out[33]=",ExpressionUUID->"0e7d10e0-4bf0-4eae-a988-480cad4d564d"]
}, Open  ]],

Cell[TextData[{
 Cell[BoxData[
  FormBox[
   RowBox[{"gt", "[", "2734", "]"}], TraditionalForm]],
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88],ExpressionUUID->
  "87d764b4-1a4b-4977-8f30-12db020f78bd"],
 StyleBox[" is a ",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 Cell[BoxData[
  FormBox[
   RowBox[{"G", "-", "tetrahedron"}], TraditionalForm]],
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88],ExpressionUUID->
  "c76f1adc-76ca-41b8-ae47-b7be1c66973e"],
 StyleBox[" representing a ",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 Cell[BoxData[
  FormBox["G", TraditionalForm]],
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88],ExpressionUUID->
  "cbc981bb-e513-4990-9888-45aa0f9d49f1"],
 StyleBox["-symbol, with vertices ",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 Cell[BoxData[
  FormBox[
   RowBox[{"2", ",", "7", ",", "4", ",", "3"}], TraditionalForm]],
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88],ExpressionUUID->
  "73819d68-22f5-47c7-9ec0-f2ec54dd03d4"],
 StyleBox[" ordered in the positive orientation.",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]]
}], "Text",
 CellChangeTimes->{{3.7692105494807243`*^9, 
  3.7692106480650682`*^9}},ExpressionUUID->"34f0b9a8-410f-4b23-b3ca-\
b7094286d421"],

Cell[TextData[StyleBox["gfReplace replace gt(2734) by G symbol, combined with \
periodic identification, e.g. [14]\[Congruent][23].",
 FontColor->RGBColor[1, 0, 1],
 Background->RGBColor[0.94, 0.91, 0.88]]], "Text",
 CellChangeTimes->{{3.7692105494807243`*^9, 3.7692106480650682`*^9}, {
  3.7692577181068788`*^9, 3.769257780270623*^9}, {3.7692591861683846`*^9, 
  3.7692592452498426`*^9}},ExpressionUUID->"22498275-f8b1-4567-bd66-\
d82439c8688e"],

Cell[BoxData[
 RowBox[{"Module", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"toG", ",", "toF"}], "}"}], ",", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"toG", "[", 
      RowBox[{"{", 
       RowBox[{"p1_", ",", "p2_", ",", "p3_", ",", "p4_"}], "}"}], "]"}], ":=", 
     RowBox[{"G", "[", 
      RowBox[{
       RowBox[{"pair", "[", 
        RowBox[{"p1", ",", "p2"}], "]"}], ",", 
       RowBox[{"pair", "[", 
        RowBox[{"p2", ",", "p3"}], "]"}], ",", 
       RowBox[{"pair", "[", 
        RowBox[{"p3", ",", "p1"}], "]"}], ",", 
       RowBox[{"pair", "[", 
        RowBox[{"p3", ",", "p4"}], "]"}], ",", 
       RowBox[{"pair", "[", 
        RowBox[{"p4", ",", "p1"}], "]"}], ",", 
       RowBox[{"pair", "[", 
        RowBox[{"p2", ",", "p4"}], "]"}]}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"toF", "[", 
      RowBox[{"{", 
       RowBox[{"p1_", ",", "p2_", ",", "p3_"}], "}"}], "]"}], ":=", 
     RowBox[{"f", "[", 
      RowBox[{
       RowBox[{"pair", "[", 
        RowBox[{"p1", ",", "p2"}], "]"}], ",", 
       RowBox[{"pair", "[", 
        RowBox[{"p2", ",", "p3"}], "]"}], ",", 
       RowBox[{"pair", "[", 
        RowBox[{"p3", ",", "p1"}], "]"}]}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"gfReplace", "=", 
     RowBox[{"starReplace", "@*", "periodicReplace", "@*", 
      RowBox[{"ReplaceAll", "[", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{
          RowBox[{"gt", "[", "nn_", "]"}], "\[RuleDelayed]", 
          RowBox[{"toG", "[", 
           RowBox[{"IntegerDigits", "[", "nn", "]"}], "]"}]}], ",", 
         RowBox[{
          RowBox[{"ft", "[", "nn_", "]"}], "\[RuleDelayed]", 
          RowBox[{"toF", "[", 
           RowBox[{"IntegerDigits", "[", "nn", "]"}], "]"}]}]}], "}"}], 
       "]"}]}]}], ";"}]}], "\[IndentingNewLine]", "]"}]], "Input",
 CellChangeTimes->{{3.7689971840062714`*^9, 3.7689974933287725`*^9}, {
   3.768997584407159*^9, 3.768997586652326*^9}, 3.769189677992587*^9, {
   3.7691897661972456`*^9, 3.7691897691800613`*^9}, {3.769209867491158*^9, 
   3.76920988528049*^9}, {3.769210452646858*^9, 3.769210538871632*^9}, 
   3.7692539977984304`*^9, {3.7692551989329314`*^9, 3.7692552417501307`*^9}},
 CellLabel->"In[34]:=",ExpressionUUID->"08c5f891-bc56-4179-b732-d32604ba46fd"],

Cell["Example code:", "Text",
 CellChangeTimes->{{3.7692593891103563`*^9, 
  3.7692593928410387`*^9}},ExpressionUUID->"052e0bf6-c799-47d2-99c6-\
7bcffa597d40"],

Cell["{gt[1234], ft[123]} // gfReplace", "Program",
 CellChangeTimes->{{3.7692578010025964`*^9, 3.769257809455573*^9}, {
   3.769257871581452*^9, 3.7692579267541404`*^9}, {3.7692590668979387`*^9, 
   3.769259090313534*^9}, 3.7692591424299583`*^9, {3.7692593302061176`*^9, 
   3.769259346684149*^9}},
 CellLabel->
  "In[127]:=",ExpressionUUID->"88743d9f-872e-45b1-8561-55b3ee9eac2a"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    SubsuperscriptBox["G", 
     RowBox[{
      FormBox[
       SuperscriptBox[
        RowBox[{"[", "12", "]"}], "*"],
       TraditionalForm], 
      FormBox[
       SuperscriptBox[
        RowBox[{"[", "23", "]"}], "*"],
       TraditionalForm], 
      FormBox[
       RowBox[{"[", "24", "]"}],
       TraditionalForm]}], 
     RowBox[{
      FormBox[
       RowBox[{"[", "12", "]"}],
       TraditionalForm], 
      FormBox[
       RowBox[{"[", "23", "]"}],
       TraditionalForm], 
      FormBox[
       SuperscriptBox[
        RowBox[{"[", "13", "]"}], "*"],
       TraditionalForm]}]], ",", 
    SubscriptBox["f", 
     RowBox[{
      FormBox[
       RowBox[{"[", "12", "]"}],
       TraditionalForm], 
      FormBox[
       RowBox[{"[", "23", "]"}],
       TraditionalForm], 
      FormBox[
       SuperscriptBox[
        RowBox[{"[", "13", "]"}], "*"],
       TraditionalForm]}]]}], "}"}], TraditionalForm]], "Program",
 CellChangeTimes->{
  3.7692578098784647`*^9, {3.7692578827609754`*^9, 3.769257895509199*^9}, 
   3.7692579270962043`*^9, {3.769259068489627*^9, 3.769259090625692*^9}, {
   3.7692591337227535`*^9, 3.769259157621477*^9}, {3.7692593363190765`*^9, 
   3.7692593466931515`*^9}},ExpressionUUID->"af3ff9eb-47f0-4886-8324-\
899cd321b0d4"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"GSDgf", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"gt", "[", "2734", "]"}], 
    RowBox[{"gt", "[", "2741", "]"}], 
    RowBox[{"gt", "[", "2671", "]"}], 
    RowBox[{"gt", "[", "1678", "]"}], 
    RowBox[{"gt", "[", "1748", "]"}], 
    RowBox[{"gt", "[", "1685", "]"}], 
    RowBox[{"ft", "[", "324", "]"}], 
    RowBox[{"ft", "[", "214", "]"}], 
    RowBox[{"ft", "[", "678", "]"}], 
    RowBox[{"ft", "[", "568", "]"}]}], "//", "gfReplace"}]}]], "Input",
 CellChangeTimes->{{3.7689963163760076`*^9, 3.7689963246581097`*^9}, {
   3.768996437926214*^9, 3.768996640784528*^9}, 3.7689966719133*^9, {
   3.7689968275390778`*^9, 3.7689968616378155`*^9}, {3.768996977425249*^9, 
   3.768997004709255*^9}, {3.768997161243208*^9, 3.768997166811055*^9}, {
   3.7689974978339033`*^9, 3.7689975205905886`*^9}, {3.7689993390144644`*^9, 
   3.7689993414211206`*^9}, {3.769211069092658*^9, 3.7692110940067134`*^9}, 
   3.7692539922488947`*^9, 3.7692540511207304`*^9, 3.7692552477476225`*^9},
 CellLabel->"In[35]:=",ExpressionUUID->"71eedc9a-6bf5-4c56-a804-5f50d5dfccc2"],

Cell[BoxData[
 FormBox[
  RowBox[{
   SubscriptBox["f", 
    RowBox[{
     FormBox[
      RowBox[{"[", "56", "]"}],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "68", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "67", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubscriptBox["f", 
    RowBox[{
     FormBox[
      RowBox[{"[", "67", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "56", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "68", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubscriptBox["f", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "12", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "23", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "24", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubscriptBox["f", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "23", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "24", "]"}],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "12", "]"}],
      TraditionalForm]}]], " ", 
   SubsuperscriptBox["G", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "56", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "27", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "68", "]"}],
      TraditionalForm]}], 
    RowBox[{
     FormBox[
      RowBox[{"[", "16", "]"}],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "67", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "17", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubsuperscriptBox["G", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "67", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "26", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "56", "]"}], "*"],
      TraditionalForm]}], 
    RowBox[{
     FormBox[
      RowBox[{"[", "16", "]"}],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "68", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "27", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubsuperscriptBox["G", 
    RowBox[{
     FormBox[
      RowBox[{"[", "26", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "27", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "56", "]"}], "*"],
      TraditionalForm]}], 
    RowBox[{
     FormBox[
      RowBox[{"[", "17", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "16", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "23", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubsuperscriptBox["G", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "17", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "12", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "16", "]"}], "*"],
      TraditionalForm]}], 
    RowBox[{
     FormBox[
      RowBox[{"[", "26", "]"}],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "67", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "27", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubsuperscriptBox["G", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "23", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      RowBox[{"[", "12", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "17", "]"}], "*"],
      TraditionalForm]}], 
    RowBox[{
     FormBox[
      RowBox[{"[", "27", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "16", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "24", "]"}], "*"],
      TraditionalForm]}]], " ", 
   SubsuperscriptBox["G", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "12", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "24", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "16", "]"}], "*"],
      TraditionalForm]}], 
    RowBox[{
     FormBox[
      RowBox[{"[", "27", "]"}],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "26", "]"}], "*"],
      TraditionalForm], 
     FormBox[
      SuperscriptBox[
       RowBox[{"[", "23", "]"}], "*"],
      TraditionalForm]}]]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.7689993268998585`*^9, 3.768999342294758*^9}, 
   3.7690154186419053`*^9, 3.769016704826116*^9, 3.769016777311424*^9, 
   3.7690173473544416`*^9, 3.769184196286643*^9, 3.7691876006106577`*^9, {
   3.769187916117728*^9, 3.7691879415244207`*^9}, 3.769189479324456*^9, 
   3.7691897746356525`*^9, 3.769189931028865*^9, 3.769189965938496*^9, 
   3.769190006722912*^9, 3.769196765247778*^9, 3.7691968215264964`*^9, 
   3.769196875681367*^9, 3.769196979538952*^9, 3.7691970858942933`*^9, {
   3.7691971565292234`*^9, 3.769197172721925*^9}, 3.769200985839651*^9, 
   3.769201252144326*^9, 3.7692102391634417`*^9, 3.7692119512769203`*^9, 
   3.769212030592733*^9, 3.769255248643176*^9, 3.7692564025394106`*^9, 
   3.7692564467094336`*^9, 3.769256865832924*^9, 3.769259133842433*^9, 
   3.7692602126809072`*^9},
 FontSize->36,
 CellLabel->"Out[35]=",ExpressionUUID->"71c83810-29a0-4ec4-aec4-ab8ffda0354c"]
}, Open  ]],

Cell[TextData[{
 StyleBox["pairSelector: divide the pair labels into the two classes of ",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 StyleBox["bulk",
  FontWeight->"Bold",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 StyleBox[" and",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 StyleBox[" bdry",
  FontWeight->"Bold",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]],
 StyleBox[" ones.",
  FontColor->RGBColor[1, 0, 1],
  Background->RGBColor[0.94, 0.91, 0.88]]
}], "Text",
 CellChangeTimes->{{3.769259603282981*^9, 3.7692596426399393`*^9}, 
   3.7692598607580996`*^9},ExpressionUUID->"5711c233-4e38-44b6-a7af-\
7062845b10b9"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"pairSelector", "[", 
    RowBox[{"pair", "[", 
     RowBox[{"a_", ",", "b_"}], "]"}], "]"}], ":=", 
   RowBox[{
    RowBox[{"If", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"a", "<", "5"}], "&&", 
       RowBox[{"b", ">", "4"}]}], ",", "##"}], "]"}], "&"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.7692117980659876`*^9, 3.769211875619938*^9}, 
   3.769254073722354*^9},
 CellLabel->"In[36]:=",ExpressionUUID->"cf8c6e09-0311-4893-8d63-a252b0a4e008"],

Cell[TextData[StyleBox["dof: Find all independent d.o.f. from the summand \
formula. (these d.o.f. are those appear in the final expression)",
 FontColor->RGBColor[1, 0, 1],
 Background->RGBColor[0.94, 0.91, 0.88]]], "Text",
 CellChangeTimes->{{3.7692594513358107`*^9, 3.7692595128936048`*^9}, {
  3.7692598526835613`*^9, 
  3.7692598538677855`*^9}},ExpressionUUID->"e424d009-e4af-4e05-aae3-\
a83e938d0a8a"],

Cell[TextData[StyleBox["GSDvd: assign d to bulk d.o.f., and v to bdry d.o.f.",
 FontColor->RGBColor[1, 0, 1],
 Background->RGBColor[0.94, 0.91, 0.88]]], "Text",
 CellChangeTimes->{{3.7692596986295547`*^9, 
  3.7692597266542916`*^9}},ExpressionUUID->"498abad1-174a-4a3f-b700-\
d22323ad01b6"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"dof", "=", 
  RowBox[{"Union", "[", 
   RowBox[{"Cases", "[", 
    RowBox[{"GSDgf", ",", 
     RowBox[{"pair", "[", "__", "]"}], ",", "\[Infinity]"}], "]"}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.7690010117370214`*^9, 3.7690010131821947`*^9}, 
   3.7690020644349604`*^9, 3.7692541426775503`*^9},
 CellLabel->"In[37]:=",ExpressionUUID->"5865c5fa-0369-4145-ab11-8196a6aaaf0f"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"[", "12", "]"}], ",", 
    RowBox[{"[", "16", "]"}], ",", 
    RowBox[{"[", "17", "]"}], ",", 
    RowBox[{"[", "23", "]"}], ",", 
    RowBox[{"[", "24", "]"}], ",", 
    RowBox[{"[", "26", "]"}], ",", 
    RowBox[{"[", "27", "]"}], ",", 
    RowBox[{"[", "56", "]"}], ",", 
    RowBox[{"[", "67", "]"}], ",", 
    RowBox[{"[", "68", "]"}]}], "}"}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.7690010144956408`*^9, 3.7690020651031303`*^9, 3.7690032265079994`*^9, 
   3.7690154275460196`*^9, {3.769016711661233*^9, 3.769016721116373*^9}, 
   3.7690167833636312`*^9, 3.7690173528753633`*^9, 3.76918419967874*^9, 
   3.769187603389105*^9, {3.769187916226411*^9, 3.769187941628193*^9}, 
   3.769189482541354*^9, 3.769189777272603*^9, 3.7691899311485476`*^9, 
   3.769189966031249*^9, 3.769190006814087*^9, 3.7691967653475137`*^9, 
   3.7691968216073055`*^9, 3.769196875779112*^9, 3.7691969796217585`*^9, 
   3.7691970859741096`*^9, {3.769197156611949*^9, 3.7691971728097267`*^9}, 
   3.7692009905785728`*^9, 3.7692012522332497`*^9, 3.7692102392911015`*^9, 
   3.769211951447465*^9, 3.769212030771242*^9, 3.7692552751172047`*^9, 
   3.7692564026381836`*^9, 3.769256446836095*^9, 3.769256866008505*^9, 
   3.769259133925412*^9, 3.769260212774658*^9},
 CellLabel->"Out[37]=",ExpressionUUID->"95369146-b8e6-44e9-9226-43f16e5b33ce"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"vd", "[", "n_pair", "]"}], ":=", 
   RowBox[{
    RowBox[{
     RowBox[{"pairSelector", "[", "n", "]"}], "[", 
     RowBox[{"dd", ",", "vv"}], "]"}], "[", "n", "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"GSDvd", "=", 
  RowBox[{"Times", "@@", 
   RowBox[{"(", 
    RowBox[{"vd", "/@", "dof"}], ")"}]}]}]}], "Input",
 CellChangeTimes->{{3.769000376052718*^9, 3.769000459538724*^9}, {
   3.7690005269465327`*^9, 3.7690005278610487`*^9}, {3.7690006746537037`*^9, 
   3.769000678673956*^9}, {3.7690008811805735`*^9, 3.7690008826945715`*^9}, {
   3.769001008269291*^9, 3.769001018370825*^9}, 3.7690020730594783`*^9, {
   3.7692541108579006`*^9, 3.7692541113356276`*^9}, 3.769254141847587*^9, {
   3.769254399572562*^9, 3.7692544080968246`*^9}, 3.7692553211998253`*^9},
 CellLabel->"In[38]:=",ExpressionUUID->"b63fb4cb-96f9-4a92-8b07-3d216ac8a274"],

Cell[BoxData[
 FormBox[
  RowBox[{
   SubscriptBox["d", 
    RowBox[{"[", "16", "]"}]], " ", 
   SubscriptBox["d", 
    RowBox[{"[", "17", "]"}]], " ", 
   SubscriptBox["d", 
    RowBox[{"[", "26", "]"}]], " ", 
   SubscriptBox["d", 
    RowBox[{"[", "27", "]"}]], " ", 
   SubscriptBox["v", 
    RowBox[{"[", "12", "]"}]], " ", 
   SubscriptBox["v", 
    RowBox[{"[", "23", "]"}]], " ", 
   SubscriptBox["v", 
    RowBox[{"[", "24", "]"}]], " ", 
   SubscriptBox["v", 
    RowBox[{"[", "56", "]"}]], " ", 
   SubscriptBox["v", 
    RowBox[{"[", "67", "]"}]], " ", 
   SubscriptBox["v", 
    RowBox[{"[", "68", "]"}]]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.769255324873869*^9, 3.7692564027049675`*^9, 
  3.769256446929843*^9, 3.7692568660623455`*^9, 3.769259133972286*^9, 
  3.769260212832486*^9},
 CellLabel->"Out[39]=",ExpressionUUID->"8f07e242-71b4-444f-b32b-331599a44314"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Algebra = ",
 Cell[BoxData[
  FormBox[
   RowBox[{
   "1", "\[CirclePlus]", "2", "\[CirclePlus]", "3", "\[CirclePlus]", "3"}], 
   TraditionalForm]],ExpressionUUID->"de4bde26-831f-4220-aece-6cd0fb0da5d3"]
}], "Section",
 CellChangeTimes->{{3.6313249645267906`*^9, 3.631324969468073*^9}, {
  3.634079929949528*^9, 3.6340799463044634`*^9}, {3.6340803880737314`*^9, 
  3.6340804022045393`*^9}, {3.634080440188712*^9, 3.634080440800747*^9}, {
  3.6340805089056425`*^9, 3.634080512095825*^9}, {3.760919749812871*^9, 
  3.76091975467457*^9}, {3.761253791403228*^9, 3.7612537945806866`*^9}, {
  3.761253930489938*^9, 3.761253983154278*^9}, {3.769187568725192*^9, 
  3.7691875687261963`*^9}, {3.769190248780648*^9, 
  3.7691902512921824`*^9}},ExpressionUUID->"93ff8b83-3c4b-468a-8ade-\
9694f281210d"],

Cell[CellGroupData[{

Cell["algebra", "Subsection",
 CellChangeTimes->{{3.7691966370101995`*^9, 
  3.769196637781313*^9}},ExpressionUUID->"048a1673-72c0-48da-8e4f-\
05d04e3dbfbe"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Arng", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"1", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"2", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"3", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"3", ",", "2"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dimA", "=", 
   RowBox[{
    RowBox[{"dim", "/@", 
     RowBox[{"First", "/@", "Arng"}]}], "//", "Total"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.6340795452505245`*^9, 3.6340795503698177`*^9}, {
   3.634079948637597*^9, 3.6340799488856115`*^9}, {3.6340804056617374`*^9, 
   3.6340804059067516`*^9}, {3.6340804445609627`*^9, 3.634080444782975*^9}, {
   3.760918963326105*^9, 3.760918983076418*^9}, {3.7612537986343365`*^9, 
   3.7612537987649374`*^9}, {3.7612539381068735`*^9, 3.7612539873728905`*^9}, 
   3.769187575257326*^9, {3.7691878751552305`*^9, 3.7691878755145054`*^9}, {
   3.7691899160288906`*^9, 3.7691899162280197`*^9}, {3.769189952026182*^9, 
   3.7691899539062686`*^9}, {3.7691899850884824`*^9, 3.7691899897468767`*^9}, 
   3.7691966472102103`*^9, {3.769196866696454*^9, 3.769196868935566*^9}, 
   3.7691969767929325`*^9, {3.7691970796265273`*^9, 3.769197083128218*^9}, {
   3.769197153213317*^9, 3.7691971678460803`*^9}, {3.769201446107791*^9, 
   3.7692014464603987`*^9}},
 CellLabel->"In[40]:=",ExpressionUUID->"b2c790dd-143f-4e15-a54a-d08ddf4d245f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"symmetryCondition", "[", "Arng", "]"}]], "Input",
 CellChangeTimes->{{3.769256218973693*^9, 3.769256222660591*^9}},
 CellLabel->"In[42]:=",ExpressionUUID->"03992745-18b8-42b1-a30e-032d0e537972"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}]}], "}"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.769256223008642*^9, 3.769256404717847*^9, 
  3.769256448982357*^9, 3.7692568661610856`*^9, 3.7692591340500402`*^9, 
  3.769260212921214*^9},
 CellLabel->"Out[42]=",ExpressionUUID->"30fc4160-525e-455c-9851-bad87197cfb5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"feq", "=", 
   RowBox[{"fEquations", "[", "Arng", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"vars", "=", 
   RowBox[{
    RowBox[{"Cases", "[", 
     RowBox[{"feq", ",", 
      RowBox[{"f", "[", "__", "]"}], ",", "\[Infinity]"}], "]"}], "//", 
    "Union"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"inst1", "=", 
  RowBox[{
   RowBox[{"FindInstance", "[", 
    RowBox[{"feq", ",", "vars"}], "]"}], "//", "Simplify"}]}]}], "Input",
 CellChangeTimes->{
  3.7692535700095177`*^9, {3.769253654975295*^9, 3.7692536635097117`*^9}, {
   3.7692562425287733`*^9, 3.769256263150132*^9}, {3.7692564338962946`*^9, 
   3.769256435217725*^9}},
 CellLabel->"In[43]:=",ExpressionUUID->"7de33e8c-8952-4912-aba9-a8264903ed60"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["2", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", "0"}], ",", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["2", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", 
      RowBox[{"-", "\[ImaginaryI]"}]}], ",", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["2", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", "\[ImaginaryI]"}], ",", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["2", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", "0"}], ",", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", "0"}], ",", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", 
      RowBox[{"-", 
       FractionBox["1", 
        RadicalBox["2", "4"]]}]}], ",", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", "0"}], ",", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm]}]],
       TraditionalForm], "\[Rule]", 
      FractionBox["1", 
       RadicalBox["2", "4"]]}]}], "}"}], "}"}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.769253579461894*^9, {3.7692536558488326`*^9, 3.769253666505721*^9}, {
   3.769256243131115*^9, 3.769256269545988*^9}, 3.769256405339143*^9, {
   3.769256436569505*^9, 3.769256449728361*^9}, 3.769256866646782*^9, 
   3.7692591342755003`*^9, 3.7692602153736563`*^9},
 CellLabel->"Out[45]=",ExpressionUUID->"0537ad72-376e-4ebb-9c45-a738e92c47fc"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"feq", "//", "Reduce"}], "//", "FullSimplify"}]], "Input",
 CellChangeTimes->{
  3.7692536934553275`*^9, {3.769256274897396*^9, 3.7692562775034013`*^9}},
 CellLabel->"In[46]:=",ExpressionUUID->"77ffbfa5-dca7-43e7-96b8-98d5023412ea"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{
       FormBox[
        SubscriptBox["f", 
         RowBox[{
          FormBox[
           SubscriptBox["3", "1"],
           TraditionalForm], 
          FormBox[
           SubscriptBox["3", "2"],
           TraditionalForm], 
          FormBox[
           SubscriptBox["3", "2"],
           TraditionalForm]}]],
        TraditionalForm], "+", 
       SqrtBox[
        RowBox[{
         FractionBox["1", 
          SqrtBox["2"]], "-", 
         SuperscriptBox[
          FormBox[
           SubscriptBox["f", 
            RowBox[{
             FormBox[
              SubscriptBox["3", "2"],
              TraditionalForm], 
             FormBox[
              SubscriptBox["3", "2"],
              TraditionalForm], 
             FormBox[
              SubscriptBox["3", "2"],
              TraditionalForm]}]],
           TraditionalForm], "2"]}]]}], "\[LongEqual]", "0"}], "\[Or]", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm]}]],
       TraditionalForm], "\[LongEqual]", 
      SqrtBox[
       RowBox[{
        FractionBox["1", 
         SqrtBox["2"]], "-", 
        SuperscriptBox[
         FormBox[
          SubscriptBox["f", 
           RowBox[{
            FormBox[
             SubscriptBox["3", "2"],
             TraditionalForm], 
            FormBox[
             SubscriptBox["3", "2"],
             TraditionalForm], 
            FormBox[
             SubscriptBox["3", "2"],
             TraditionalForm]}]],
          TraditionalForm], "2"]}]]}]}], ")"}], "\[And]", 
   RowBox[{
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "+", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], "\[LongEqual]", "0"}], "\[And]", 
   RowBox[{
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "+", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm]}], "\[LongEqual]", "0"}], "\[And]", 
   RowBox[{
    FormBox[
     SubscriptBox["f", 
      RowBox[{
       FormBox[
        SubscriptBox["2", "1"],
        TraditionalForm], 
       FormBox[
        SubscriptBox["3", "2"],
        TraditionalForm], 
       FormBox[
        SubscriptBox["3", "2"],
        TraditionalForm]}]],
     TraditionalForm], "\[LongEqual]", "0"}], "\[And]", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["2", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm]}]],
       TraditionalForm], "\[LongEqual]", 
      RowBox[{"-", "\[ImaginaryI]"}]}], "\[Or]", 
     RowBox[{
      FormBox[
       SubscriptBox["f", 
        RowBox[{
         FormBox[
          SubscriptBox["2", "1"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "2"],
          TraditionalForm], 
         FormBox[
          SubscriptBox["3", "1"],
          TraditionalForm]}]],
       TraditionalForm], "\[LongEqual]", "\[ImaginaryI]"}]}], ")"}], "\[And]", 
   RowBox[{
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "+", 
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm]}], "\[LongEqual]", "0"}], "\[And]", 
   RowBox[{
    FormBox[
     SubscriptBox["f", 
      RowBox[{
       FormBox[
        SubscriptBox["2", "1"],
        TraditionalForm], 
       FormBox[
        SubscriptBox["3", "1"],
        TraditionalForm], 
       FormBox[
        SubscriptBox["3", "1"],
        TraditionalForm]}]],
     TraditionalForm], "\[LongEqual]", "0"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.7692536941414824`*^9, 3.769256280177598*^9, 
  3.769256405783942*^9, 3.7692564500864377`*^9, 3.7692568670357075`*^9, 
  3.7692591343921595`*^9, 3.769260215867337*^9},
 CellLabel->"Out[46]=",ExpressionUUID->"8c5b056b-048c-464c-ad79-ec44b8ab6476"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Compute GSD", "Subsection",
 CellChangeTimes->{{3.7692563605160236`*^9, 
  3.769256365661254*^9}},ExpressionUUID->"388e3c93-1017-4466-bf41-\
d3e722ad4bd7"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"symbolReplace", "=", 
   RowBox[{"ReplaceAll", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       RowBox[{"pair", "[", 
        RowBox[{"a_", ",", "b_"}], "]"}], "\[RuleDelayed]", 
       RowBox[{"Symbol", "[", 
        RowBox[{"\"\<p\>\"", "<>", 
         RowBox[{"ToString", "[", "a", "]"}], "<>", 
         RowBox[{"ToString", "[", "b", "]"}]}], "]"}]}], ",", 
      RowBox[{"SuperStar", "->", "Identity"}]}], "}"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"sumrng", "[", "n_pair", "]"}], ":=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"symbolReplace", "@", "n"}], ",", 
     RowBox[{
      RowBox[{"pairSelector", "[", "n", "]"}], "[", 
      RowBox[{"rng", ",", "Arng"}], "]"}]}], "}"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.7690015366450367`*^9, 3.7690016657588873`*^9}, {
   3.7690154627530174`*^9, 3.7690154710034943`*^9}, {3.769015506029516*^9, 
   3.769015512319931*^9}, {3.7691876332983336`*^9, 3.7691876351706295`*^9}, {
   3.7691878095842676`*^9, 3.7691878296368833`*^9}, {3.7692099684629307`*^9, 
   3.76920996940845*^9}, {3.7692115916103945`*^9, 3.769211592665927*^9}, {
   3.7692119165315094`*^9, 3.769211936935345*^9}, {3.76921201183816*^9, 
   3.7692120141559134`*^9}, 3.769254072642665*^9, {3.7692545509316516`*^9, 
   3.7692545515280576`*^9}, 3.7692553004009867`*^9, {3.769255361975209*^9, 
   3.7692553643293686`*^9}},
 CellLabel->"In[47]:=",ExpressionUUID->"fea1536d-04e9-4fe2-aae0-ff02808e4615"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"toSum", "=", 
  RowBox[{"Join", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"GSDgf", " ", "GSDvd"}], "//", "symbolReplace"}], "}"}], ",", 
    RowBox[{"sumrng", "/@", "dof"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.7690015034238377`*^9, 3.7690015038985257`*^9}, {
   3.769001674241457*^9, 3.769001780859239*^9}, 3.769002084698793*^9, 
   3.769003281637065*^9, {3.769015608817374*^9, 3.7690156090407877`*^9}, 
   3.7692115916213646`*^9, 3.7692541418526025`*^9, 3.7692545509336195`*^9, 
   3.769255775881664*^9},
 CellLabel->"In[49]:=",ExpressionUUID->"6a735220-b629-4133-8ad2-ebe477065c24"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     SubscriptBox["d", "p16"], " ", 
     SubscriptBox["d", "p17"], " ", 
     SubscriptBox["d", "p26"], " ", 
     SubscriptBox["d", "p27"], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p12",
        TraditionalForm], 
       FormBox["p23",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm]}]], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p23",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm], 
       FormBox["p12",
        TraditionalForm]}]], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p56",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm], 
       FormBox["p67",
        TraditionalForm]}]], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p67",
        TraditionalForm], 
       FormBox["p56",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm]}]], " ", 
     SubscriptBox["v", "p12"], " ", 
     SubscriptBox["v", "p23"], " ", 
     SubscriptBox["v", "p24"], " ", 
     SubscriptBox["v", "p56"], " ", 
     SubscriptBox["v", "p67"], " ", 
     SubscriptBox["v", "p68"], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p12",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p27",
        TraditionalForm], 
       FormBox["p26",
        TraditionalForm], 
       FormBox["p23",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p56",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p16",
        TraditionalForm], 
       FormBox["p67",
        TraditionalForm], 
       FormBox["p17",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p67",
        TraditionalForm], 
       FormBox["p26",
        TraditionalForm], 
       FormBox["p56",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p16",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p17",
        TraditionalForm], 
       FormBox["p12",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p26",
        TraditionalForm], 
       FormBox["p67",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p26",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm], 
       FormBox["p56",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p17",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm], 
       FormBox["p23",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p23",
        TraditionalForm], 
       FormBox["p12",
        TraditionalForm], 
       FormBox["p17",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p27",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm]}]]}], ",", 
    RowBox[{"{", 
     RowBox[{"p12", ",", 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "1"},
         {"2", "1"},
         {"3", "1"},
         {"3", "2"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p16", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p17", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p23", ",", 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "1"},
         {"2", "1"},
         {"3", "1"},
         {"3", "2"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p24", ",", 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "1"},
         {"2", "1"},
         {"3", "1"},
         {"3", "2"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p26", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p27", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p56", ",", 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "1"},
         {"2", "1"},
         {"3", "1"},
         {"3", "2"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p67", ",", 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "1"},
         {"2", "1"},
         {"3", "1"},
         {"3", "2"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p68", ",", 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "1"},
         {"2", "1"},
         {"3", "1"},
         {"3", "2"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]}], "}"}]}], "}"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{
  3.7690015050605154`*^9, 3.7690016770810723`*^9, 3.769001711321918*^9, 
   3.769001751103458*^9, 3.7690017813339653`*^9, {3.7690020329854493`*^9, 
   3.7690020392688723`*^9}, 3.7690020852154384`*^9, 3.769003282701217*^9, 
   3.769015438884515*^9, 3.7690154765712667`*^9, 3.7690155167042775`*^9, 
   3.769015609848618*^9, 3.769016806428561*^9, 3.7690173623592453`*^9, 
   3.7690175505871077`*^9, 3.769184207039341*^9, {3.7691876147118573`*^9, 
   3.7691876383796387`*^9}, {3.7691879164989963`*^9, 3.7691879418358154`*^9}, 
   3.7691897865863504`*^9, 3.7691899313636065`*^9, 3.769189966250662*^9, 
   3.769190007043746*^9, 3.76919676559688*^9, 3.7691968218237457`*^9, 
   3.769196876012529*^9, 3.7691969798441367`*^9, 3.769197086183564*^9, {
   3.7691971568254213`*^9, 3.769197173035688*^9}, 3.769201017461443*^9, 
   3.769201252459668*^9, 3.769210239468626*^9, 3.7692119516678047`*^9, 
   3.7692120310165863`*^9, 3.769255385240484*^9, 3.7692557772130833`*^9, 
   3.769255815055191*^9, 3.769256405884673*^9, 3.7692564503237705`*^9, 
   3.769256867127512*^9, 3.7692591345327845`*^9, 3.7692602159600873`*^9},
 CellLabel->"Out[49]=",ExpressionUUID->"ad38c533-4e08-418d-90dd-430047fd7c15"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{"Inactive", "[", "Sum", "]"}], "@@", "toSum"}], ")"}], "/.", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"a_Integer", ",", "b_Integer"}], "}"}], "\[RuleDelayed]", 
   SubscriptBox["a", "b"]}]}]], "Input",
 CellChangeTimes->{{3.7690019640850725`*^9, 3.769001993101823*^9}, {
  3.7690021288300934`*^9, 3.76900215287127*^9}},
 CellLabel->"In[50]:=",ExpressionUUID->"5df97a33-ce73-460f-9039-01260848821d"],

Cell[BoxData[
 FormBox[
  RowBox[{
   TemplateBox[{"Sum"},
    "InactiveHead",
    BaseStyle->"InactiveTraditional",
    SyntaxForm->"Symbol",
    Tooltip->"Inactive[Sum]"], "[", 
   RowBox[{
    RowBox[{
     SubscriptBox["d", "p16"], " ", 
     SubscriptBox["d", "p17"], " ", 
     SubscriptBox["d", "p26"], " ", 
     SubscriptBox["d", "p27"], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p12",
        TraditionalForm], 
       FormBox["p23",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm]}]], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p23",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm], 
       FormBox["p12",
        TraditionalForm]}]], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p56",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm], 
       FormBox["p67",
        TraditionalForm]}]], " ", 
     SubscriptBox["f", 
      RowBox[{
       FormBox["p67",
        TraditionalForm], 
       FormBox["p56",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm]}]], " ", 
     SubscriptBox["v", "p12"], " ", 
     SubscriptBox["v", "p23"], " ", 
     SubscriptBox["v", "p24"], " ", 
     SubscriptBox["v", "p56"], " ", 
     SubscriptBox["v", "p67"], " ", 
     SubscriptBox["v", "p68"], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p12",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p27",
        TraditionalForm], 
       FormBox["p26",
        TraditionalForm], 
       FormBox["p23",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p56",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p16",
        TraditionalForm], 
       FormBox["p67",
        TraditionalForm], 
       FormBox["p17",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p67",
        TraditionalForm], 
       FormBox["p26",
        TraditionalForm], 
       FormBox["p56",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p16",
        TraditionalForm], 
       FormBox["p68",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p17",
        TraditionalForm], 
       FormBox["p12",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p26",
        TraditionalForm], 
       FormBox["p67",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p26",
        TraditionalForm], 
       FormBox["p27",
        TraditionalForm], 
       FormBox["p56",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p17",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm], 
       FormBox["p23",
        TraditionalForm]}]], " ", 
     SubsuperscriptBox["G", 
      RowBox[{
       FormBox["p23",
        TraditionalForm], 
       FormBox["p12",
        TraditionalForm], 
       FormBox["p17",
        TraditionalForm]}], 
      RowBox[{
       FormBox["p27",
        TraditionalForm], 
       FormBox["p16",
        TraditionalForm], 
       FormBox["p24",
        TraditionalForm]}]]}], ",", 
    RowBox[{"{", 
     RowBox[{"p12", ",", 
      RowBox[{"{", 
       RowBox[{
        SubscriptBox["1", "1"], ",", 
        SubscriptBox["2", "1"], ",", 
        SubscriptBox["3", "1"], ",", 
        SubscriptBox["3", "2"]}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p16", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p17", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p23", ",", 
      RowBox[{"{", 
       RowBox[{
        SubscriptBox["1", "1"], ",", 
        SubscriptBox["2", "1"], ",", 
        SubscriptBox["3", "1"], ",", 
        SubscriptBox["3", "2"]}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p24", ",", 
      RowBox[{"{", 
       RowBox[{
        SubscriptBox["1", "1"], ",", 
        SubscriptBox["2", "1"], ",", 
        SubscriptBox["3", "1"], ",", 
        SubscriptBox["3", "2"]}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p26", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p27", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p56", ",", 
      RowBox[{"{", 
       RowBox[{
        SubscriptBox["1", "1"], ",", 
        SubscriptBox["2", "1"], ",", 
        SubscriptBox["3", "1"], ",", 
        SubscriptBox["3", "2"]}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p67", ",", 
      RowBox[{"{", 
       RowBox[{
        SubscriptBox["1", "1"], ",", 
        SubscriptBox["2", "1"], ",", 
        SubscriptBox["3", "1"], ",", 
        SubscriptBox["3", "2"]}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"p68", ",", 
      RowBox[{"{", 
       RowBox[{
        SubscriptBox["1", "1"], ",", 
        SubscriptBox["2", "1"], ",", 
        SubscriptBox["3", "1"], ",", 
        SubscriptBox["3", "2"]}], "}"}]}], "}"}]}], "]"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{3.7692560775206785`*^9, 3.7692564059534903`*^9, 
  3.76925645041652*^9, 3.769256867194318*^9, 3.7692591345836496`*^9, 
  3.7692602160379143`*^9},
 FontSize->24,
 CellLabel->"Out[50]=",ExpressionUUID->"3c31cfe6-12f6-44cb-b1fd-8ca142a0abbe"]
}, Open  ]],

Cell[TextData[StyleBox["list all f-values for the solution inst1. define fn \
as the function with these values.",
 FontColor->RGBColor[1, 0, 1],
 Background->RGBColor[0.94, 0.91, 0.88]]], "Text",
 CellChangeTimes->{{3.7692599450970354`*^9, 
  3.7692600110164785`*^9}},ExpressionUUID->"c11dfac3-50fb-478f-874f-\
41e5e7b031a0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"fsol1", "=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"#", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "\[Rule]", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"#", "[", 
          RowBox[{"[", "2", "]"}], "]"}], "/.", 
         RowBox[{"inst1", "[", 
          RowBox[{"[", "1", "]"}], "]"}]}], ")"}]}], "&"}], "/@", 
     RowBox[{"symmetryCondition", "[", "Arng", "]"}]}], ")"}], "\[Union]", 
   RowBox[{"inst1", "[", 
    RowBox[{"[", "1", "]"}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.7690149107666435`*^9, 3.769014937004937*^9}, {
  3.7690149802146606`*^9, 3.7690151026189194`*^9}, {3.7690151822274055`*^9, 
  3.769015191324847*^9}, {3.769015311240292*^9, 3.769015383070998*^9}, {
  3.7692554229335713`*^9, 3.769255469317665*^9}, {3.769255532943163*^9, 
  3.769255558050187*^9}},
 CellLabel->"In[51]:=",ExpressionUUID->"31232459-7e8b-4541-9bc7-3b17c034d2a9"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     RowBox[{"-", "\[ImaginaryI]"}]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "\[ImaginaryI]"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "\[ImaginaryI]"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     RowBox[{"-", 
      FractionBox["1", 
       RadicalBox["2", "4"]]}]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     RowBox[{"-", "\[ImaginaryI]"}]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     RowBox[{"-", 
      FractionBox["1", 
       RadicalBox["2", "4"]]}]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     RowBox[{"-", "\[ImaginaryI]"}]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "\[ImaginaryI]"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     RowBox[{"-", 
      FractionBox["1", 
       RadicalBox["2", "4"]]}]}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["1", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "1"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["2", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "1"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", "0"}], ",", 
    RowBox[{
     FormBox[
      SubscriptBox["f", 
       RowBox[{
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm], 
        FormBox[
         SubscriptBox["3", "2"],
         TraditionalForm]}]],
      TraditionalForm], "\[Rule]", 
     FractionBox["1", 
      RadicalBox["2", "4"]]}]}], "}"}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.7690149373450484`*^9, {3.7690149820327888`*^9, 3.7690151048412285`*^9}, 
   3.769015191862368*^9, {3.769015322264811*^9, 3.7690153547879705`*^9}, 
   3.7690153852395*^9, 3.769184127371031*^9, 3.76918765378273*^9, {
   3.7691879166566687`*^9, 3.769187941989913*^9}, 3.769189791117594*^9, 
   3.769189931494288*^9, 3.7691899663716936`*^9, 3.7691900072716737`*^9, 
   3.769196765862135*^9, 3.769196821951396*^9, 3.769196876164159*^9, 
   3.769196979974823*^9, 3.7691970863052497`*^9, {3.7691971569819603`*^9, 
   3.7691971731992517`*^9}, 3.769201252596362*^9, 3.7692102397678285`*^9, 
   3.7692119518752236`*^9, 3.7692120312190447`*^9, 3.7692555591780195`*^9, 
   3.76925582909277*^9, 3.7692564061774025`*^9, 3.7692564505192795`*^9, 
   3.769256867266142*^9, 3.7692591346434546`*^9, 3.7692602161226544`*^9},
 CellLabel->"Out[51]=",ExpressionUUID->"c9ab5e0e-c361-42a2-aa54-1f937158c38c"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"Clear", "[", "fn", "]"}], ";", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"fn", "@@", "#1"}], ")"}], "\[Rule]", 
      RowBox[{"N", "[", "#2", "]"}]}], "&"}], "@@@", "fsol1"}], "//", 
   RowBox[{"ReplaceAll", "[", 
    RowBox[{"Rule", "\[Rule]", "Set"}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.7690160306935024`*^9, 3.7690160476337767`*^9}, {
   3.769016219536574*^9, 3.769016226729396*^9}, 3.769187931357303*^9, {
   3.769201034831087*^9, 3.76920108606896*^9}},
 CellLabel->"In[52]:=",ExpressionUUID->"c313408e-283b-4f29-8c55-66b6ed04e3e2"],

Cell[TextData[StyleBox["Assign the numeric values and evaluate the sum.",
 FontColor->RGBColor[1, 0, 1],
 Background->RGBColor[0.94, 0.91, 0.88]]], "Text",
 CellChangeTimes->{{3.7692601317549443`*^9, 
  3.7692601474918113`*^9}},ExpressionUUID->"25d3407d-ffb6-40f5-9525-\
a7d80c0bcc43"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"toSumN", "=", 
   RowBox[{"toSum", "/.", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"G", "\[Rule]", "mTet"}], ",", 
      RowBox[{"dd", "\[Rule]", "dim"}], ",", 
      RowBox[{"vv", "\[Rule]", "v"}], ",", 
      RowBox[{"f", "\[Rule]", "fn"}]}], "}"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"(", 
   RowBox[{"Sum", "@@", "toSumN"}], ")"}], "/", 
  RowBox[{"dimA", "^", "2"}]}]}], "Input",
 CellChangeTimes->{{3.769016095269146*^9, 3.769016103935975*^9}, {
   3.769016365610551*^9, 3.7690163669629755`*^9}, {3.7690176296557875`*^9, 
   3.7690176374251666`*^9}, 3.7692115916283565`*^9, 3.769254141858585*^9, 
   3.7692545509366407`*^9, {3.769255852368664*^9, 3.7692558548987675`*^9}, {
   3.7692600977633038`*^9, 3.7692601281375623`*^9}, {3.7692601923771987`*^9, 
   3.7692601936816816`*^9}},
 CellLabel->"In[53]:=",ExpressionUUID->"11e0066d-1308-4f40-8833-ddc907bb0ec2"],

Cell[BoxData[
 FormBox[
  RowBox[{"6.`", "\[VeryThinSpace]", "+", 
   RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.7690161062696457`*^9, 3.769016371367581*^9, 3.7690170156786776`*^9, 
   3.769017463834327*^9, 3.769017566838172*^9, 3.76901772694738*^9, 
   3.7690193369105177`*^9, 3.7691841705769467`*^9, 3.7691842154915514`*^9, 
   3.7691876635580873`*^9, {3.769187916909995*^9, 3.769187942131569*^9}, 
   3.769189798803582*^9, 3.769189931634033*^9, 3.7691899665153093`*^9, 
   3.7691900074610395`*^9, 3.769196766235173*^9, 3.7691968220241957`*^9, 
   3.7691968763366623`*^9, 3.7691969801363907`*^9, 3.769197086474785*^9, {
   3.769197157210402*^9, 3.7691971734068146`*^9}, 3.769201252701131*^9, 
   3.76921023991846*^9, 3.769211952106646*^9, 3.769212031451421*^9, 
   3.769255878779331*^9, 3.769256406334979*^9, 3.7692564506489005`*^9, 
   3.769256867353901*^9, 3.7692591347711487`*^9, 3.7692601063764973`*^9, 
   3.769260239903815*^9},
 CellLabel->"Out[54]=",ExpressionUUID->"36e3eb7f-dab6-42db-af33-4ce191182f2c"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1352, 817},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
TaggingRules->{
 "PresenterSettings" -> {
   "ShowToolbar" -> True, "SlideBreakStyles" -> {}, "ShowSlideBreaks" -> 
    True}},
Magnification:>1.1 Inherited,
FrontEndVersion->"11.3 for Microsoft Windows (64-bit) (March 28, 2018)",
StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", 
  CharacterEncoding -> "UTF-8"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 161, 3, 75, "Section",ExpressionUUID->"132e4493-406b-4308-8399-c3bf8ea88b51"],
Cell[744, 27, 297, 6, 44, "Input",ExpressionUUID->"9e4172bc-bde2-4648-ae13-44c16a1f17a1"],
Cell[1044, 35, 365, 5, 44, "Input",ExpressionUUID->"81ab6ff9-ca9a-4954-9600-2e9e961cc842"],
Cell[CellGroupData[{
Cell[1434, 44, 155, 3, 36, "Subsection",ExpressionUUID->"724d96c4-149e-49ae-8f53-191d21a8ab3a"],
Cell[1592, 49, 644, 19, 46, "Input",ExpressionUUID->"7e9b4097-c922-49b8-bcab-752c6b187e59"],
Cell[2239, 70, 3304, 84, 177, "Input",ExpressionUUID->"ea16ee10-22ab-4a3c-8ff8-50ff9985785c"],
Cell[5546, 156, 156, 3, 38, "Text",ExpressionUUID->"f5370a3d-88d1-4d53-880f-e4ac59f6d10b"],
Cell[5705, 161, 368, 6, 44, "Program",ExpressionUUID->"15474eb2-a3df-4e8c-8c5d-885fd0ed7de6"],
Cell[6076, 169, 652, 14, 48, "Program",ExpressionUUID->"0166f5e8-a0cd-4911-b13b-1cfb98ffee6c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6765, 188, 171, 3, 36, "Subsection",ExpressionUUID->"fc3a3eb1-0373-43f1-b9b7-ae025de72511"],
Cell[6939, 193, 1817, 42, 111, "Input",ExpressionUUID->"e1a2d00d-55aa-48ff-be81-8eb442de04c4"],
Cell[8759, 237, 157, 3, 38, "Text",ExpressionUUID->"1c85a93a-e29a-4cfc-b0df-52bd1af9a438"],
Cell[8919, 242, 199, 3, 44, "Program",ExpressionUUID->"99826ed3-794d-4221-bfa2-c90bc43b5757"],
Cell[9121, 247, 1258, 36, 77, "Program",ExpressionUUID->"47439685-50e6-4681-8788-8098dc6d3937"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10416, 288, 161, 3, 36, "Subsection",ExpressionUUID->"d062233e-ab35-436c-8397-4f624d662e24"],
Cell[10580, 293, 519, 15, 41, "Text",ExpressionUUID->"6476039f-c022-4201-9ed5-c73fa8551f6d"],
Cell[11102, 310, 374, 8, 44, "Input",ExpressionUUID->"1275223a-9d3c-4510-81af-6c33d2a1ba15"],
Cell[11479, 320, 2450, 63, 184, "Input",ExpressionUUID->"693f93e7-df28-422e-ab77-b288ba00ed27"],
Cell[13932, 385, 262, 5, 38, "Text",ExpressionUUID->"15f29ffb-a0de-4803-a6b6-7980e92cb94e"],
Cell[14197, 392, 846, 20, 67, "Input",ExpressionUUID->"775cbdb4-e11a-407a-a954-f3da23689fb5"],
Cell[15046, 414, 478, 12, 44, "Input",ExpressionUUID->"a87ae13f-f866-4de8-b286-e6a69eb5d105"],
Cell[15527, 428, 440, 9, 44, "Input",ExpressionUUID->"da788df7-0e8b-4f92-a8f2-7951243cf2d5"],
Cell[15970, 439, 3632, 84, 133, "Input",ExpressionUUID->"d17c2cc3-2389-478f-a9aa-dccb6c2eaa37"],
Cell[19605, 525, 799, 18, 67, "Input",ExpressionUUID->"f5532cde-9b8d-4cc9-b0de-274b901d924f"],
Cell[20407, 545, 2259, 53, 89, "Input",ExpressionUUID->"f72d4a6e-35cc-4236-a746-7cbae7b24f60"]
}, Open  ]],
Cell[CellGroupData[{
Cell[22703, 603, 257, 4, 36, "Subsection",ExpressionUUID->"35a69115-fb7e-4cfa-95db-d287edb75b84"],
Cell[22963, 609, 873, 20, 38, "Text",ExpressionUUID->"bd6f3f66-2730-4f53-a9ab-4d4b25b0350a"],
Cell[CellGroupData[{
Cell[23861, 633, 1972, 50, 111, "Input",ExpressionUUID->"cad7a18d-5ba0-4426-b6fe-afb1e104bad8"],
Cell[25836, 685, 3268, 77, 64, "Output",ExpressionUUID->"0e7d10e0-4bf0-4eae-a988-480cad4d564d"]
}, Open  ]],
Cell[29119, 765, 1433, 39, 38, "Text",ExpressionUUID->"34f0b9a8-410f-4b23-b3ca-b7094286d421"],
Cell[30555, 806, 446, 7, 38, "Text",ExpressionUUID->"22498275-f8b1-4567-bd66-d82439c8688e"],
Cell[31004, 815, 2306, 57, 133, "Input",ExpressionUUID->"08c5f891-bc56-4179-b732-d32604ba46fd"],
Cell[33313, 874, 159, 3, 36, "Text",ExpressionUUID->"052e0bf6-c799-47d2-99c6-7bcffa597d40"],
Cell[33475, 879, 382, 6, 44, "Program",ExpressionUUID->"88743d9f-872e-45b1-8561-55b3ee9eac2a"],
Cell[33860, 887, 1313, 45, 57, "Program",ExpressionUUID->"af3ff9eb-47f0-4886-8324-899cd321b0d4"],
Cell[CellGroupData[{
Cell[35198, 936, 1081, 21, 42, "Input",ExpressionUUID->"71eedc9a-6bf5-4c56-a804-5f50d5dfccc2"],
Cell[36282, 959, 5776, 215, 155, "Output",ExpressionUUID->"71c83810-29a0-4ec4-aec4-ab8ffda0354c"]
}, Open  ]],
Cell[42073, 1177, 748, 21, 36, "Text",ExpressionUUID->"5711c233-4e38-44b6-a7af-7062845b10b9"],
Cell[42824, 1200, 503, 14, 42, "Input",ExpressionUUID->"cf8c6e09-0311-4893-8d63-a252b0a4e008"],
Cell[43330, 1216, 407, 7, 36, "Text",ExpressionUUID->"e424d009-e4af-4e05-aae3-a83e938d0a8a"],
Cell[43740, 1225, 290, 5, 36, "Text",ExpressionUUID->"498abad1-174a-4a3f-b700-d22323ad01b6"],
Cell[CellGroupData[{
Cell[44055, 1234, 405, 9, 42, "Input",ExpressionUUID->"5865c5fa-0369-4145-ab11-8196a6aaaf0f"],
Cell[44463, 1245, 1398, 27, 42, "Output",ExpressionUUID->"95369146-b8e6-44e9-9226-43f16e5b33ce"]
}, Open  ]],
Cell[CellGroupData[{
Cell[45898, 1277, 899, 19, 64, "Input",ExpressionUUID->"b63fb4cb-96f9-4a92-8b07-3d216ac8a274"],
Cell[46800, 1298, 890, 26, 46, "Output",ExpressionUUID->"8f07e242-71b4-444f-b32b-331599a44314"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[47751, 1331, 810, 16, 75, "Section",ExpressionUUID->"93ff8b83-3c4b-468a-8ade-9694f281210d"],
Cell[CellGroupData[{
Cell[48586, 1351, 157, 3, 36, "Subsection",ExpressionUUID->"048a1673-72c0-48da-8e4f-05d04e3dbfbe"],
Cell[48746, 1356, 1458, 30, 64, "Input",ExpressionUUID->"b2c790dd-143f-4e15-a54a-d08ddf4d245f"],
Cell[CellGroupData[{
Cell[50229, 1390, 218, 3, 42, "Input",ExpressionUUID->"03992745-18b8-42b1-a30e-032d0e537972"],
Cell[50450, 1395, 23768, 947, 123, "Output",ExpressionUUID->"30fc4160-525e-455c-9851-bad87197cfb5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[74255, 2347, 765, 19, 85, "Input",ExpressionUUID->"7de33e8c-8952-4912-aba9-a8264903ed60"],
Cell[75023, 2368, 3574, 128, 82, "Output",ExpressionUUID->"0537ad72-376e-4ebb-9c45-a738e92c47fc"]
}, Open  ]],
Cell[CellGroupData[{
Cell[78634, 2501, 266, 5, 42, "Input",ExpressionUUID->"77ffbfa5-dca7-43e7-96b8-98d5023412ea"],
Cell[78903, 2508, 5758, 216, 90, "Output",ExpressionUUID->"8c5b056b-048c-464c-ad79-ec44b8ab6476"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[84710, 2730, 161, 3, 36, "Subsection",ExpressionUUID->"388e3c93-1017-4466-bf41-d3e722ad4bd7"],
Cell[84874, 2735, 1506, 33, 64, "Input",ExpressionUUID->"fea1536d-04e9-4fe2-aae0-ff02808e4615"],
Cell[CellGroupData[{
Cell[86405, 2772, 637, 13, 42, "Input",ExpressionUUID->"6a735220-b629-4133-8ad2-ebe477065c24"],
Cell[87045, 2787, 8412, 266, 133, "Output",ExpressionUUID->"ad38c533-4e08-418d-90dd-430047fd7c15"]
}, Open  ]],
Cell[CellGroupData[{
Cell[95494, 3058, 462, 11, 42, "Input",ExpressionUUID->"5df97a33-ce73-460f-9039-01260848821d"],
Cell[95959, 3071, 5836, 211, 189, "Output",ExpressionUUID->"3c31cfe6-12f6-44cb-b1fd-8ca142a0abbe"]
}, Open  ]],
Cell[101810, 3285, 326, 6, 36, "Text",ExpressionUUID->"c11dfac3-50fb-478f-874f-41e5e7b031a0"],
Cell[CellGroupData[{
Cell[102161, 3295, 948, 23, 42, "Input",ExpressionUUID->"31232459-7e8b-4541-9bc7-3b17c034d2a9"],
Cell[103112, 3320, 23915, 926, 201, "Output",ExpressionUUID->"c9ab5e0e-c361-42a2-aa54-1f937158c38c"]
}, Open  ]],
Cell[127042, 4249, 628, 15, 42, "Input",ExpressionUUID->"c313408e-283b-4f29-8c55-66b6ed04e3e2"],
Cell[127673, 4266, 285, 5, 36, "Text",ExpressionUUID->"25d3407d-ffb6-40f5-9525-a7d80c0bcc43"],
Cell[CellGroupData[{
Cell[127983, 4275, 929, 21, 64, "Input",ExpressionUUID->"11e0066d-1308-4f40-8833-ddc907bb0ec2"],
Cell[128915, 4298, 1065, 17, 42, "Output",ExpressionUUID->"36e3eb7f-dab6-42db-af33-4ce191182f2c"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

